Hi Mariusz Kocierz (mk310935),
Greetings. Thank you for posting the thread to our community.
Based on your description, it seems you want to download and install Microsoft 365 with your school account.
As far as I know, generally, to properly download and install the Office desktop app, first you’ll need the corresponding license called “The latest desktop version of Office” in your school account. You can sign into the Office portal: My account with your school account and check your Microsoft 365 licenses:

If you meet the perquisite above, you can go to the App & devices page in Office portal to download your Office:

Here is also the corresponding support article as reference for your as well: Download, install, or reinstall Microsoft 365, Office 2024, or Office 2021 on a PC or Mac - Microsoft Support.
If you have further queries or my explanation above causes misunderstanding to you, Please be free to contact and send feedback to me. I’m willing to help you any time.
Hope you having a nice day and wish you a brilliant year ahead as well😊!
Sincerely,
Harry | Microsoft Community Moderator